How Many Spectral Lines are Produced During Electron Transitions in Hydrogen?

[vkash]

no of line in line spectrum is equal to jumps of electron from one shell to another. Am i correct.

IN my book it is written that if a electron in hydrogen jumps from n₁ to n₂ then number of spectral lines is given by formula {(n₁-n₂)(n₁-n₂+1}/2. so consider a electron jump from 4^th shell to 2^nd shell then number of kinds of jump can be (1) 4^th to 3^rd,(2) 4^th to 2^nd So there are only two jumps. but if we apply formula then it will come out to be 3. So where i or formula is wrong.
thanks for any kind of help.

 

[SpectraCat]

no of line in line spectrum is equal to jumps of electron from one shell to another. Am i correct.

IN my book it is written that if a electron in hydrogen jumps from n₁ to n₂ then number of spectral lines is given by formula {(n₁-n₂)(n₁-n₂+1}/2. so consider a electron jump from 4^th shell to 2^nd shell then number of kinds of jump can be (1) 4^th to 3^rd,(2) 4^th to 2^nd So there are only two jumps. but if we apply formula then it will come out to be 3. So where i or formula is wrong.
thanks for any kind of help.

what about 3rd to 2nd?

 

[vkash]

what about 3rd to 2nd?

dear 4^th 3^rd and 2^nd represent the energy level of hydrogen atom n₁ and n₂ represent the given energy level. Do you got it.

 

[SpectraCat]

dear 4^th 3^rd and 2^nd represent the energy level of hydrogen atom n₁ and n₂ represent the given energy level. Do you got it.

Yes, "I got it". You asked what the "third" transition was that is possible in the manifold of levels including 4,3, and 2. I told you the answer. The formula is correct, you just missed a transition with your initial analysis.

 

[vkash]

Yes, "I got it". You asked what the "third" transition was that is possible in the manifold of levels including 4,3, and 2. I told you the answer. The formula is correct, you just missed a transition with your initial analysis.

what's that transition is that 3^rd to 2^nd. other transitions are already mentioned above.

 

[SpectraCat]

what's that transition is that 3^rd to 2^nd. other transitions are already mentioned above.

Do you understand what you already wrote? I mean from the 3rd shell to the 2nd shell. Just like you "already mentioned" 4th shell to 3rd shell, and 4th shell to 2nd shell.

Draw yourself a picture, using stacked horizontal lines to represent the states (2, 3 and 4), and downward arrows to represent the transitions. You should see that there are 3 possibilities almost immediately.